一种新的求解复杂多目标优化问题的进化算法

New Evolutionary Algorithm for Complicated Multiobjective Optimization

复杂多目标优化问题通常有大量的Pareto有效解,并且存在部分Pareto有效解容易求出,而部分Pareto有效解很难得到的情况。已有的多目标进化算法在设计进化算子时都没有考虑Pareto有效解的求解难易程度,都是使用固定的杂交变异概率,因而在求解复杂多目标优化问题时效率不高。用带权重的极大、极小策略,通过专门设计的权重得到一组适应值函数,同时进一步构造了随进化代数变化的杂交、变异概率,其大小根据求解有效解的难易程度自动调节,提出的多目标进化算法的效率大大提高,并能求出有效界面上相对均匀分布的有效解。数值仿真表明了本算法非常有效。

There are usually a lot of Pareto optimal solutions in a complicated multiobjective optimization,and some parts of them are easily to get,but others are not.At present,existing multiobjective evolutionary algorithms neglect the level of difficulty in solving Pareto optimal solutions,and they make use of fixed crossover and mutation probability in all parts,which is not efficient.Using a weighted min-max strategy,a group of fitness functions with the specially designed weight were obtained,and changing crossover and mutation probability following along with evolutionary generation were constructed.The crossover and mutation probability can be automatically regulated according to the level of difficulty in solving Pareto optimal solutions for a problem.Thus the proposed algorithm can enhance performance of algorithm and obtain evenly distributed Pareto optimal solutions.The numerical simulations show the proposed algorithm is very efficient.